Rastrigin Function

Its a multi-modal version of DeJong/Spherical function, characterized by deep local minima arranged as sinusoidal bumps. An optimization algorithm can easily become trapped in local minimum on its way to the global minimizer.

It is multi-modal function
Minima : [0, 0, ..., 0]
Maxima : 1210.6
Maximum Dimensionality : 30

Function definition

3D plot

    clc; clear
    x = -5:0.1:5; y = -5:0.1:5;
    xy=zeros(length(x)*length(y),2);
    cntpts=0;
    for ii=1:length(x)
        for jj=1:length(y)
            cntpts=cntpts+1;
            xy(cntpts,1:2)=[x(ii),y(jj)];
        end
    end
    funval = Rastrigin([xy]);
    funval = reshape(funval, length(y),length(x));
    surfc(x, y, funval)

Other Useful Functions

DeJong Rosenbrock Ackley Alpine Rastrigin Griewank Schaffer